There is no prerequisite in DSP to be able to do DSP with JUCE. If you have already some background there, in my opinion you can already start learning all the JUCE basic stuff, how to make a plug-in on the UI side for example. Then, if you don’t know how to do a specific thing in DSP, you might look for other resources eventually.

Just start something! Depending on what you’re working on, you’ll have to learn some (or a lot of) DSP, but cross that bridge when you get there. Trying to slog your way through an entire book before you even start is a recipe for losing interest and quitting. Especially that book - it’s a fine book, but it uses the author’s personal alternative to JUCE, so a lot of what it teaches is done a totally different way with JUCE